Hausdorff School on Log-correlated Fields

Details

Log-correlated fields, and in particular their extreme values, have rich properties due to their multiscale nature. They form a universality class with many realizations in physics and mathematics – the twodimensional Gaussian free field being the simplest example. Results of the past ten years exhibit properties similar to log-correlated fields in

branching Brownian motions,

the logarithm of a characteristic polynomial of a random matrix

the values of Riemann zeta on the critical line

The study of these problems is often interrelated, importing ideas from random matrix theory, analytic number theory, and stochastic processes, and benefits from physical arguments like the replica trick and the study of random energy landscapes, sometimes leading to far-reaching conjectures. This summer school aims at giving a unified introduction of these topics in light of the recent advances. It consists of three mini-courses, completed by a small number of research talks, and short talks by young researchers.